高考中一类静电场题剖析

剖析高考中一类静电场题的出题特点,以此帮助学生从不同角度认识同、异号点电荷的连线和垂线上场强和电势分布特征.     

一个数学问题的探究

文[1]最后提出了一个待解决的数学问题:过∠MON(∠MON=θ,θ为定值,且θ∈(0,π))内一定点P做直线l分别交射线OM、ON于A、B两点(A、B异于顶点O),求|OA|+|OB|-|AB|的取值范围.     

钛扩散铌酸锂矩形波导中的双折射耦合对传播常数的影响

 从亥姆霍兹方程出发，得到了各向异性光波导在弱导近似下的耦合模理论。耦合系数包括偏振耦合项和双折射耦合项。并用马卡提里近似下的模式作为零级近似。用一级微扰法计算了折射率渐变分布的钛扩散铌酸锂矩形波导的传播常数。在给定参数的情况下，得到双折射项引起的传播常数的改变约为主微扰项的3%，因此双折射耦合对钛扩散铌酸锂矩形波导的性能影响不可忽略，这对设计和分析与它相关的光波导器件具有指导意义。     

最佳跳频序列族的设计与分析

本文提出了基于ｐ元广义ＧＭＷ序列和ｐ元Ｋａｓａｍｉ序列构造跳频序列族的方法,证明了基于广义ＧＭＷ序列所构造的跳频序列族具有最佳Ｈａｍｍｉｎｇ相关特性,而基于Ｋａｓａｍｉ序列所构造的跳频序列族不具有最佳Ｈａｍｍｉｎｇ相关特性。     

矩阵乘积的Schur余的奇异值估计

本文得到了矩阵乘积的Ｓｃｈｕｒ余的奇异值的一些不等式，改进了近期的一些结果．     

STRUCTURES OF Si AND Ge CLUSTERS UNDER MODIFIED STILLINGER-WEBER POTENTIAL

Structural behaviors of silicon and germanium clusters under the recently proposed modified Stillinger-Weber (SW) potential have been studied by molecular dynamics method along with the con-jugate-gradient optimization. Since the SW potentials have been derived from the properties of bulk materials, it gives relatively large discrepancy when the cluster number is small, e.g. n=3 and 4. When n>4, the ground-state structures under the modified SW potential are close to that from the first-principle calculation. The binding energies are also improved under the modified SW potential. These results may be attributed to the relative enhancement of the two-body term over the three-body term in the modified SW potential, which leads to structures with a preferential coordination number 4. Structural behaviors of germanium clusters are similar to those of silicon.     

环形轴对称锐边界等离子体的扭曲模不稳定性

本文对任意环径比、任意β值、任意截面形状的轴对称锐边界等离子体,给出了正确的边界条件,导出了无导体壳和存在导体壳两种情况下扭曲模稳定性的能量矩阵,对环向波数n为1,2,3的能量矩阵,给出了可快速、精确积分的具体形式,对不同环径比和不同拉长度b/α的椭圆形、跑道形(包括圆形)截面的等离子体进行了数值计算。计算结果表明,跑道形截面等离子体的临界β值比相应的椭圆形截面的β值高,随着b/α的增大,跑道形截面的临界β值也增加。导体壳有一定的稳定作用。从系统稳定性边缘态的本征矢量来看,存在导体壳时极向扰动的最大分量是模数1的扰动。与J.P.Freidberg和W.Grossmann的工作比较,在环径比为2时,圆截面等离子体的临界β值相差23％,临界q值相差15％。     

环结构中的若干新成果(一)

代数结构的理论发展起来后,Artin,E.在环中引进极小条件,建立了具极小条件的半单纯环与单纯环的结构理论,被誉为是抽象代数中仅次于Galois理论的工作。对称地,Goldie与Lesieur and Croisot等又建立了具极大条件的半质环的结构理论,其结果也是很漂亮的。     

Preparation and characterization of SiO_2/TiO_2/methylcellulose hybrid thick films for optical waveguides

Optical-quality films of a few μm thickness are a basic re- quirement for integrated optics[1-3]. Since such films are thick by normal coating standards, a number of special- ized methods have been developed to form them. The sol-gel processing is one approach because of the high optical quality of materials produced and freedom to im- pregnate them with a variety of additives to modify their optical characteristics. It is a popular and widespread technique for preparing coating films in labo…